The funny pic thread

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    tuoder

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    teknickle

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    Or mathematically, the area of a square is the square of any side or S^2; 1^2=1, in this case.

    The area of a circle is pi x radius, squared. The radius is 0.5. Squared, that's 0.25. Multiplied by pi, that's 0.785.

    If the area of the square was equal to the area of the circle, those numbers would be equal. :)

    Actually, the moment the first corners were inverted, it was no longer a square. (so the method for calculating area becomes that of a polygon).

    The inside area will constantly change (reduced) as each line is broken into a smaller lines (always perpendicular).
    The point of it is that you can approximate (VERY closely) the perimeter of what will be a "near circle" to be 4.
    Just imagine a pixelated circle. As long as it remains 90 degree angles, the perimeter will be 4. (even if the lines become so short that it looks like an aliased circle).
    And as that happens, its area will become that of the circle (that is to say, you can take this out to 10^20 decimal places of precision..and it still won't be EXACTLY the same---but right above it).
    The circle is the moment you intersect those 90 degree vectors with one continuous line.
    Please keep in mind that you are supposed to continually reduce the line segments to near infinity.
    If you do, it truly does look like a circle and takes on the same area.
     

    Bill of Rights

    Cogito, ergo porto.
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    7   0   0
    Apr 26, 2008
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    Where's the bacon?
    Actually, the moment the first corners were inverted, it was no longer a square. (so the method for calculating area becomes that of a polygon).

    The inside area will constantly change (reduced) as each line is broken into a smaller lines (always perpendicular).
    The point of it is that you can approximate (VERY closely) the perimeter of what will be a "near circle" to be 4.
    Just imagine a pixelated circle. As long as it remains 90 degree angles, the perimeter will be 4. (even if the lines become so short that it looks like an aliased circle).
    And as that happens, its area will become that of the circle (that is to say, you can take this out to 10^20 decimal places of precision..and it still won't be EXACTLY the same---but right above it).
    The circle is the moment you intersect those 90 degree vectors with one continuous line.
    Please keep in mind that you are supposed to continually reduce the line segments to near infinity.
    If you do, it truly does look like a circle and takes on the same area.

    I didn't invert any corners... just calculated the area of a square of side "1" and the area of a circle with circumference π (although I forgot to put the symbol in my formula you quoted above.) The difference in area of them is 0.858407.

    And truth be told, I think we should have calculated perimeter and circumference, not area of either one. ;)
     
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